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TitlePiecewise algebraic curve
TypeArticle in Journal
AbstractA piecewise algebraic curve is defined by a bivariate spline function. Using the techniques of the B-net form of bivariate splines function, discriminant sequence of polynomial (cf. Yang Lu et al. (Sci. China Ser. E 39(6) (1996) 628) and Yang Lu et al. (Nonlinear Algebraic Equation System and Automated Theorem Proving, Shanghai Scientific and Technological Education Publishing House, Shanghai, 1996)) and the number of sign changes in the sequence of coefficients of the highest degree terms of sturm sequence, we determine the number of real intersection points of two piecewise algebraic curves whose common points are finite. A lower bound of the number of real intersection points is given in terms of the method of rotation degree of vector field.
KeywordsRotation degree, Application in algebraic curves, discriminant sequence, Number of real intersection points
URL http://www.sciencedirect.com/science/article/pii/S0377042701005672
JournalJournal of Computational and Applied Mathematics
Pages277 - 289
NoteSelected papers of the Int. Symp. on Applied Mathematics, August 2000, Dalian, China
Translation No
Refereed No